Data and code underlying the publication: Physics-Informed Neural Networks for Solving Forward and Inverse Problems in Complex Beam Systems.

Research ObjectivesThe primary research objective of the study is to explore the application of physics-informed neural networks (PINNs) in predicting the displacement and rotations of a double beam based on Euler-Bernoulli and Timoshenko theories under various load conditions. The research aims to demonstrate the accuracy and efficiency of PINNs in handling forward and inverse problems involving partial differential equations (PDEs), even with a limited number of training points and the presence of noise in the data. This objective is to introduce physics informed machine learning techniques in structural engineering contexts specifically beam dynamics.<br>Type of ResearchThe research focuses on the practical implementation of theoretical concepts in machine learning and structural engineering. It leverages computational methods to solve real-world engineering problems, demonstrating the utility of PINNs in predicting structural behaviors accurately and efficiently. The study combines elements of machine learning and structural engineering by leveraging the physical knowledge of beam dynamics.<br>Method of Data CollectionData collection in this study involves the generation of synthetic data through forward PINNs simulations. This data includes displacement and rotation measurements of a double Timoshenko beam subjected to different loading conditions. The study also introduces Gaussian noise into the data to test the robustness of the PINN model. Additionally, the researchers compare their results with those obtained from traditional numerical methods and other machine learning approaches to validate their findings.<br>Type of DataFor the forward problem, a well-posed physical equation is needed, while for the inverse problem, data from the forward problem is utilized. For validating the forward and inverse problems, we have an analytic closed-form solution which is explicitly mentioned in the Python notebooks. All implementations of the proposed methodology are on Jupyter Python notebooks. To run the notebooks, only need to execute the cells with Shift+Enter.

一、研究目标
本研究的核心目标为探索基于物理信息的神经网络（Physics-Informed Neural Networks, PINNs）在不同载荷条件下，基于欧拉-伯努利（Euler-Bernoulli）与铁木辛柯（Timoshenko）梁理论预测双梁位移与转角的应用场景。本研究旨在验证PINNs在处理含偏微分方程（Partial Differential Equations, PDEs）的正问题与逆问题时的准确性与效率，即便训练点数量有限且数据中存在噪声。本研究的另一目标是将基于物理信息的机器学习技术引入结构工程领域，尤其是梁动力学方向。

二、研究类型
本研究聚焦于机器学习与结构工程领域理论概念的落地实践，通过计算方法解决实际工程问题，验证PINNs在精准高效预测结构力学行为方面的应用价值。本研究结合机器学习与结构工程的相关要素，依托梁动力学的物理知识开展研究。

三、数据采集方法
本研究的数据采集环节通过正向PINNs仿真生成合成数据集，数据集涵盖不同载荷条件下双铁木辛柯梁的位移与转角测量数据。本研究还向数据中引入高斯噪声，以测试PINN模型的鲁棒性。此外，研究者将模型结果与传统数值方法及其他机器学习方法得到的结果进行对比，以验证研究结论的有效性。

四、数据类型
对于正问题，需采用适定的物理方程；对于逆问题，则使用正问题生成的数据。为验证正、逆问题的求解效果，本研究配备了解析闭式解，相关内容已在Jupyter Python笔记本中明确给出。本研究所提方法的所有实现均基于Jupyter Python笔记本，运行该笔记本时仅需通过Shift+Enter执行对应单元格即可。